Handbook of logic in artificial intelligence and logic programming (vol. 3)
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
A linear-time transformation of linear inequalities into conjunctive normal form
Information Processing Letters
Nonmonotonic reasoning: from complexity to algorithms
Annals of Mathematics and Artificial Intelligence
On Stratified Belief Base Compilation
Annals of Mathematics and Artificial Intelligence
Compiling propositional weighted bases
Artificial Intelligence - Special issue on nonmonotonic reasoning
System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
A survey on knowledge compilation
AI Communications
Journal of Artificial Intelligence Research
Preferred subtheories: an extended logical framework for default reasoning
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Inconsistency management and prioritized syntax-based entailment
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Weakening conflicting information for iterated revision and knowledge integration
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
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This paper sheds light on the lexicographic inference from stratified belief bases which is known to have desirable properties from theoretical, practical and psychological points of view. However, this inference is expensive from the computational complexity side. Indeed, it amounts to a $\Delta_2^p$-complete problem. In order to tackle this hardness, we propose in this work a new compilation of the lexicographic inference using the so-called Boolean cardinality constraints. This compilation enables a polynomial time lexicographic inference and offers the possibility to update the priority relation between the strata without any re-compilation. Moreover, it can be efficiently extended to deal with the lexicographical closure inference which takes an important place in default reasoning. Furthermore, unlike the existing compilation approaches of the lexicographic inference, ours can be efficiently parametrized by any target compilation language. In particular, it enables to take advantage of the well-known prime implicates language which has been quite influential in artificial intelligence and computer science in general.